We develop a non-perturbative theory to study large-scale quantum dynamics of Dirac particles in disordered scalar potentials (the so-called topological metal). For general disorder strength and carrier doping, we find that at large times, superdiffusion occurs. I.e., the mean squared displacement grows as $sim tln t$. In the static limit, our analytical theory shows that the conductance of a finite-size system obeys the scaling equation identical to that found in previous numerical studies. These results suggest that in the topological metal, there exist some transparent channels -- where waves propagate freely -- dominating long-time transport of the system. We discuss the ensuing consequence -- the transverse superdiffusion in photonic materials -- that might be within the current experimental reach.
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